Diffractive optical element and optical system having the same

ABSTRACT

In a diffractive optical element, which is formed by laminating at least three layers of diffraction gratings made of at least three kinds of materials which differ in dispersion, at least three design wavelengths are set.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates to a diffractive optical elementhaving such a grating structure that a light flux of a useful wavelengthregion concentrates at a specific order (design order), and to anoptical system having the diffractive optical element.

[0003] 2. Description of Related Art

[0004] While it has been practiced to abate a chromatic aberration of anoptical system by combining different lens materials, another method forabating a chromatic aberration by arranging, on a lens surface or withinan optical system, a diffractive optical element (or a diffractiongrating) having a diffracting function was disclosed in opticalliterature, such as “International Lens Design Conference (1990)”, SPIEVol. 1354, etc., and the publications of Japanese Laid-Open PatentApplications No. HEI 4-213421 and No. HEI 6-324262 and U.S. Pat. No.5,044,706. This method is based on a physical phenomenon that adirection in which a chromatic aberration takes place for rays of lightof a certain wavelength region on a refractive surface becomes inverseto that on a diffractive surface.

[0005] Comparing a refractive surface (lens surface) with a diffractivesurface in respect of the function on rays of incident light, one ray oflight remains one after refraction on the refractive surface, whereasone ray of light is split into a plurality of rays of different orderswhen it is diffracted by the diffractive surface. Therefore, in using adiffractive optical element, the structure of grating of the diffractiveoptical element is decided in such a way as to cause a light flux of auseful wavelength region to concentrate at a specific diffraction order(hereinafter referred to as the design order). With a light fluxconcentrating at a specific diffraction order, such as a + first orderor a − first order, rays of diffraction light of orders other than thespecific diffraction order have a low degree of intensity. When theintensity of the rays becomes zero, the diffraction light ceases toexist.

[0006] In enhancing the efficiency of diffraction for a diffractionlight of an m-th order, a phase difference giving structure is arrangedto give a phase difference of 2 πm to rays of each optical path in thediffracting direction. The rays of light are then caused by thisarrangement to interfere each other and are thus intensified.

[0007]FIG. 12 shows a structural arrangement of a transmission typediffractive optical element 1. In the diffractive optical element 1, thegrating thickness of a diffraction grating 3 is assumed to be d and therefractive index of the material of the diffraction grating 3 is assumedto be n. In order to give the phase difference of 2 πm to light of awavelength λ of an m-th order of diffraction, the structural arrangementis required to satisfy the following condition:

2 πm=2 πd(n−1)/λ  (1).

[0008] In a case where the condition of the formula (1) above isestablished at each pitch of the grating, the diffraction efficiencybecomes higher.

[0009] The actual structure of the diffractive optical element which isnecessary for attaining this diffracting function is called a kinoform.There are various known modes of arranging the kinoform structure. Inone known mode, spans for which the phase difference of 2 πm is givenare arranged to continue one after another. In another known mode, acontinuous phase difference distribution of kinoform is approximatedstepwise in a binary shape. In a further known mode, a minute periodicstructure of kinoform is approximated in a triangular wave shape. Eachof these structures is arranged either on the surface of a flat plate oron a convex or concave lens surface within an optical system. Further,the diffractive optical element of this type is manufactured, forexample, with a mold prepared by a semiconductor manufacturing processsuch as lithography or by machining or with a replica formed on thebasis of such a mold.

[0010] The diffractive optical element is capable of greatly abating achromatic aberration taking place on a refractive surface due todispersion by a glass material. The diffractive optical element can bearranged to have a great aberration abating effect, like an asphericlens, by varying the period of its periodic structure.

[0011] In the case of the prior example mentioned above, variousaberrations, particularly a chromatic aberration, are lessened by theeffect of diffraction. The effect attained by including the diffractiveoptical element in an optical system can be confirmed, for example, on adrawing showing aberrations or the like. However, if the diffractionefficiency is not high for the diffraction light of the design order, nolight might be existing there in actuality. It is, therefore, necessaryto have a sufficiently high diffraction efficiency for diffraction lightof design order. Further, in a case where there is any light havingdiffraction orders other than the design order, that light is imaged ata different part from where the light of the design order is imaged.Such a light thus becomes flare light to lower the contrast of an image.Therefore, it is important, for any optical system that is designed toutilize a diffraction effect, to sufficiently consider a spectraldistribution of diffraction efficiency and the behavior of light ofdiffraction orders than the design order.

[0012]FIG. 13 shows the spectral characteristic of diffractionefficiency obtained for a specific diffraction order with thediffractive optical element shown in FIG. 12 formed on a certain surfacewithin an optical system. In FIG. 13, the abscissa axis indicateswavelength and the ordinate axis indicates the diffraction efficiency.The diffractive optical element is designed to have the diffractionefficiency become highest at the first order of diffraction (shown in afull line curve in FIG. 13). In other words, the design order is thefirst order. FIG. 13 further shows the diffraction efficiency fordiffraction orders near the design order, i.e., the zero order and thesecond order ((1±1)-th order). As shown in FIG. 13, at the design order,the diffraction efficiency becomes highest at a certain wavelength(hereinafter referred to as a “design wavelength”) and graduallydecreases at other wavelengths. The reason for this is as follows. Thegrating thickness required for making the phase difference 2π is asexpressed by the formula (1). In a case where the grating thickness isset to satisfy the condition of this formula for the design wavelength,this condition becomes somewhat unsatisfied for other wavelengths,thereby causing a drop in diffraction efficiency.

[0013] The drop portion of the diffraction efficiency at the designorder becomes diffraction light of other orders and comes to appear asflare light. In a case where the diffractive optical element is providedwith a plurality of diffraction gratings, the drop in diffractionefficiency at wavelengths other than the design wavelength eventuallycauses a decrease in transmission factor.

[0014] In view of the above problem, the inventor of the presentinvention has developed a diffractive optical element, as disclosed inJapanese Patent Application No. HEI 8-307154, which has a gratingstructure as shown in FIG. 18. In the grating structure shown in FIG.13, a plurality of diffraction gratings including a first diffractiongrating 3 a and a second diffraction grating 3 b, which are made of atleast two kinds of materials which differ in dispersion, overlap eachother. With the diffractive optical element arranged in this manner, itsdiffraction efficiency remains high at the design order over the wholeregion of useful wavelengths, as shown in FIG. 19.

[0015] Another diffractive optical element formed by overlaying on eachother diffraction gratings of materials of two different kinds wasdisclosed in U.S. Pat. No. 5,017,000, etc. This optical element,however, relates to a multiple focus lens and nothing has been disclosedwith respect to how to enhance its diffraction efficiency.

[0016] Further, the publications of Japanese Laid-Open PatentApplications No. HEI 9-127321 and No. HEI 9-127322 have discloseddiffractive optical elements arranged to prevent color fluctuations andgeneration of flare light due to light of unnecessary diffraction ordersby lowering the wavelength dependency of the diffraction efficiency.More specifically, the diffractive optical element is formed bylaminating a plurality of different optical materials (two or threeoptical materials) with one or two relief patterns formed at theboundary face between the different optical materials.

[0017] In the diffractive optical element disclosed in the aboveJapanese Laid-Open Patent Application No. HEI 9-127321 or No. HEI9-127322, there are two wavelengths at which the phase amplitude becomes“1”, as shown in FIG. 15. The diffractive optical element is thusarranged, on the basis of these wavelengths, to have two optimizedwavelengths (design wavelengths) where the maximum diffractionefficiency can be obtained. FIG. 16 shows the diffraction efficiencyobtained at the design order, and FIG. 17 shows the diffractionefficiency obtained at diffraction orders in the neighborhood of thedesign order. Since there are two design wavelengths, the diffractionefficiency trends downward at either of two ends of the usefulwavelength region of 400 nm to 700 nm. In the case of FIG. 16, thediffraction efficiency drops to a level of 94% or thereabout on the sideof longer wavelengths. Then, in inverse proportion to the diffractionefficiency shown in FIG. 16, the diffraction efficiency obtained atdiffraction orders in the neighborhood of the design order increases upto 2% or thereabout on the side of longer wavelengths, as shown in FIG.17.

[0018] Therefore, the use of the diffractive optical element, underspecial service conditions, for the useful wavelength region of 400 nmto 700 nm has not been always satisfactory for reducing the amount ofgeneration of flare light due to light of unnecessary orders. Thediffractive optical element thus has been desired to have a higherdiffraction efficiency over the useful wavelength region. Theabove-stated special service conditions include, for example, a casewhere the diffractive optical element having the above-stateddiffraction efficiency is applied to a photo-taking lens of a camera orthe like. In the case of the camera, a film is used on an evaluationplane and there are various photo-taking conditions (object and exposureconditions) occurring. Among such various conditions, in the event of,for example, a light source of a high degree of luminance existing at apart of the object, the high luminance light source is saturated morethan an exposure apposite to the film while an apposite exposure isadjusted to other parts of the object in taking a shot. In that event,since the exposure for the light source is several times as much as theapposite exposure, even a slight amount of diffraction light of ordersnear the design order might be multiplied several times. Then, theslight amount of diffraction light tends to result in flare light aroundthe light source, like a halo.

BRIEF SUMMARY OF THE INVENTION

[0019] It is an object of the invention to provide a diffractive opticalelement, or an optical system having the diffractive optical element,which has a high diffraction efficiency over the whole useful wavelengthregion with the amount of unnecessary diffraction light made small.

[0020] To attain the above object, in accordance with an aspect of theinvention, there is provided a diffractive optical element, which isformed by laminating at least three layers of diffraction gratings madeof at least three kinds of materials which differ in dispersion, whereinat least three design wavelengths are set.

[0021] The diffractive optical element according to the invention hasthe following features.

[0022] In the diffractive optical element according to the invention,the above-mentioned at least three layers of diffraction gratings arelaminated on a base plate, and, letting the diffraction gratings beassumed to be a first diffraction grating, a second diffraction gratingand an L-th diffraction grating, as counted from the base plate, agrating thickness of the first diffraction grating be denoted by d1, agrating thickness of the second diffraction grating be denoted by d2, agrating thickness of the L-th diffraction grating be denoted by dL, arefractive index of the first diffraction grating at a wavelength λ bedenoted by n1(λ), a refractive index of the second diffraction gratingat the wavelength λ be denoted by n2(λ), a refractive index of the L-thdiffraction grating at the wavelength λ be denoted by nL(λ), anarbitrary wavelength within a useful wavelength region be denoted by λ0,and a design order of diffraction be denoted by m, it is preferable tosatisfy the following condition:

0.9217≦{(n 1(λ0)−1)d 1±(n 2(λ0)−1)d 2± . . . ±(nL(λ0)−1)dL}/mλ0≦1.0783.

[0023] Further, in the diffractive optical element according to theinvention, the above-mentioned at least three layers of diffractiongratings are laminated on a base plate, and, letting the diffractiongratings be assumed to be a first diffraction grating, a seconddiffraction grating and an L-th diffraction grating, as counted from thebase plate, a grating thickness of the first diffraction grating bedenoted by d1, a grating thickness of the second diffraction grating bedenoted by d2, a grating thickness of the L-th diffraction grating bedenoted by dL, a refractive index of the first diffraction grating at awavelength λ be denoted by n1(λ), a refractive index of the seconddiffraction grating at the wavelength λ be denoted by n2(λ), arefractive index of the L-th diffraction grating at the wavelength λ bedenoted by nL(λ), an arbitrary wavelength within a useful wavelengthregion be denoted by λ0, and a design order of diffraction be denoted bym, it is preferable to satisfy the following condition:

0.8755≦{(n 1(λ0)−1)d 1±(n 2(λ0)−1)d 2± . . . ±(nL(λ0)−1)dL}/mλ0≦1.1245.

[0024] In a mode of the diffractive optical element according to theinvention, the design wavelengths include at least two designwavelengths which are shorter than a center wavelength of a usefulwavelength region.

[0025] In another mode of the diffractive optical element according tothe invention, the useful wavelength region is a visible spectrum.

[0026] In a further mode of the diffractive optical element according tothe invention, the diffraction gratings made of at least three kinds ofmaterials which differ in dispersion include at least one kind ofgrating structure whose grating thickness within one period monotonouslyincreases between materials which differ in dispersion and at least onekind of grating structure whose grating thickness within one periodmonotonously decreases between materials which differ in dispersion.

[0027] In a still further mode of the diffractive optical elementaccording to the invention, the first diffraction grating and the baseplate are made of the same material.

[0028] Further, there is provided an optical system as a part of whichone of the above diffractive optical elements according to the inventionis used. The optical system includes, in particular, an image formingoptical system and an observation optical system.

[0029] The above and other objects and features of the invention willbecome apparent from the following detailed description of preferredembodiments thereof taking in connection with the accompanying drawings.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING

[0030]FIG. 1 is a plan view showing essential parts of a diffractiveoptical element according to a first embodiment of the invention.

[0031]FIG. 2 is a sectional view taken along a line A-A′ of FIG. 1.

[0032]FIG. 3 is a graph for explaining the phase amplitude of thediffractive optical element according to the first embodiment.

[0033]FIG. 4 is a graph showing the diffraction efficiency obtained at adesign order of the diffractive optical element according to the firstembodiment.

[0034]FIG. 5 is a graph showing the diffraction efficiency obtained atorders near the design order of the diffractive optical elementaccording to the first embodiment.

[0035]FIG. 6 shows a diffractive lens to which the diffractive opticalelement according to the first embodiment is applied.

[0036]FIG. 7 is a sectional view showing a binary grating shape relatedto the diffractive optical element according to the first embodiment.

[0037]FIG. 8 is a sectional view showing essential parts of adiffractive optical element according to a second embodiment of theinvention.

[0038]FIG. 9 is a sectional view showing essential parts of adiffractive optical element according to a third embodiment of theinvention.

[0039]FIG. 10 schematically shows an optical system using thediffractive optical element according to a fourth embodiment of theinvention.

[0040]FIG. 11 schematically shows another optical system using thediffractive optical element according to a fifth embodiment of theinvention.

[0041]FIG. 12 is a sectional view showing by way of example thearrangement of essential parts of the conventional diffractive opticalelement.

[0042]FIG. 13 is a graph showing the diffraction efficiency of theconventional diffractive optical element.

[0043]FIG. 14 is a sectional view showing another example ofconventional diffractive optical element.

[0044]FIG. 15 is a graph showing the phase amplitude of the conventionaldiffractive optical element of FIG. 14.

[0045]FIG. 16 is a graph showing the diffraction efficiency obtained ata design order of the conventional diffractive optical element of FIG.14.

[0046]FIG. 17 is a graph showing the diffraction efficiency obtained atorders near the design order of the conventional diffractive opticalelement of FIG. 14.

[0047]FIG. 18 is a sectional view showing essential parts of adiffractive optical system disclosed in Japanese Patent Application No.HEI 8-307154.

[0048]FIG. 19 is a graph showing the diffraction efficiency of thediffractive optical system disclosed in Japanese Patent Application No.HEI 8-307154.

DETAILED DESCRIPTION OF THE INVENTION

[0049] Hereinafter, preferred embodiments of the invention will bedescribed in detail with reference to the drawings.

[0050]FIG. 1 is a front-view showing a diffractive optical elementaccording to a first embodiment of the invention. Referring to FIG. 1,the diffractive optical element 1 is composed of a diffraction gratingpart 3 formed on the surface of a base plate 2.

[0051]FIG. 2 is a sectional view of the diffractive optical elementtaken along a line A-A′ of FIG. 1. The diffractive optical element 1 isshown in a shape which is exaggerated in the direction of depth ofdiffraction gratings. The sectional shape of the diffractive opticalelement 1 includes a first diffraction grating 3 a formed on the baseplate 2, a second diffraction grating 3 b formed on the firstdiffraction grating 3 a, and a third diffraction grating 3 c formed onthe second diffraction grating 3 b. These diffraction gratings 3 a, 3 band 3 c are laminated one on top of another.

[0052] Further, the shape of each diffraction grating in the firstembodiment is such that the grating thickness of the first and thirddiffraction gratings 3 a and 3 c is arranged to monotonously decreasefrom left to right within one period, as viewed in FIG. 2, while thegrating thickness of the second diffraction grating 3 b is arranged tomonotonously increase within one period. Thus, at least one diffractiongrating of the two kinds of grating shapes differently changing thegrating thickness is overlaid upon another diffraction grating which isof the other grating shape.

[0053] Next, a combination of the materials of the first, second andthird diffraction gratings 3 a, 3 b and 3 c and a grating shape by whichthe diffraction efficiency can be enhanced at the design order of adiffractive optical element over a wide region of wavelengths aredescribed as follows.

[0054] In the case of an ordinary transmission type single-layerdiffraction grating which is to be used in air, as shown in FIG. 12, acondition for maximizing the diffraction efficiency for a design wavelength λ0 is as follows. When a light flux is perpendicularly incidenton the diffraction grating 3, the optical path length difference d0between the crest and the trough of the diffraction grating 3 isarranged to be integer times as much as the design wavelength λ0, asexpressed below:

d 0=(n 0−1)d=mλ0  (2)

[0055] where n0 represents the refractive index of the material at thewavelength λ0, d represents a grating thickness (difference between themaximum thickness and the minimum thickness of the diffraction grating),and m represents the number of a diffraction order.

[0056] When light of a wavelength λ is perpendicularly incident on thediffraction grating which has an optical path length difference d(A),the diffraction efficiency η of the ordinary single-layer diffractiveoptical element can be expressed as follows:

η=sin c ² {d(λ)/mλ−1}=sin c ²{(n(λ)−1)d/mλ−1}  (3)

[0057] where n(λ) represents the refractive index of the materialobtained at the wavelength λ.

[0058] A multilayer diffractive optical element which is composed of twoor more layers is fundamentally the same as the single-layer diffractiveoptical element. In order to have the multilayer diffractive opticalelement act as one diffraction grating through all the component layers,an optical path length difference d(λ) is obtained from the gratingthickness of each diffraction grating. Then, with the optical pathlength difference values obtained for all the layers are added togetherto obtain a sum. The multilayer diffractive optical element is formed insuch a way as to make the sum integer times as large as the designwavelength. In FIG. 2, the first embodiment is arranged to be athree-layer diffractive optical element. However, the invention is notlimited to this structure but is applicable to a diffraction gratingstructure composed of more than three laminated layers. In this case,the grating thickness is assumed to be a difference between the maximumthickness and the minimum thickness within one period of eachdiffraction grating, and the refractive index at the wavelength λ0 ofthe material of the L-th layer is assumed to be n0L. Then, a formulawhich applies to a multilayer diffractive optical element andcorresponds to the formula (2) can be expressed as follows:

n 01−1)d 1±(n 02−1)d 2± . . . ±(n 0 L−1)dL=mλ0  (4).

[0059] The same condition that has been described above for thesingle-layer diffractive optical element applies also to the multilayerlaminated type diffractive optical element from the viewpoint of adifference in optical path length. In the case of the multilayerdiffractive optical element, when light of a wavelength λ isperpendicularly incident on the diffraction grating having the opticalpath length difference d(λ), its diffraction efficiency η becomes asexpressed by the following formula:

η=sin c ² {d(λ)/mλ−1}=sin c ²[{(n 1(λ)−1)d 1±(n 2(λ)−1)d 2± . . .±(nL(λ)−1)dL}/mλ−1]  (5)

[0060] where nL(λ) represents the refractive index obtained at thewavelength λ of the material of the L-th layer, i.e., the L-thdiffraction grating.

[0061] With diffraction of light to the left from the zero-orderdiffraction light as viewed in FIG. 2 assumed to be in a positivediffraction order, the sign “±” shown in the formula (5) above becomesas follows. A grating shape in which the thickness of grating decreasesfrom the left to the right as viewed in FIG. 2, i.e., the shape of thediffraction gratings 3 a and 3 c, is deemed to be in the positivedirection of diffraction. Conversely, a grating shape in which thegrating thickness increases from the left to the right, i.e., the shapeof the diffraction grating 3 b, is deemed to be in the negativedirection of diffraction.

[0062] It is a feature of the invention that there are three wavelengthsat which the diffraction efficiency is at a maximum rate to satisfy theformula (4) within the useful wavelength region, that is, there arethree design wavelengths. Compared with the arrangements of the priorexample, the arrangement of the invention gives a higher rate ofdiffraction efficiency over the whole region of useful wavelengths.

[0063] The embodiment of the invention is further described on the basisof its practical arrangement by way of example as follows. In the caseof one example, the useful wavelength region is a visual spectrum, thedesign order of the diffraction grating is a + first order (m=1), andthere are three design wavelengths. In this case, at least three kindsof materials which differ in dispersion are required. For simplificationof description, the diffractive optical element is assumed to be of aminimum feasible structure composed of three layers of diffractiongratings made of three different kinds of materials.

[0064] With the useful wavelength region assumed to be the visiblespectrum, the diffractive optical element is assumed to have threedesign wavelengths, i.e., a wavelength of 410 nm, the wavelength ofF-line and the wavelength of C-line. In this case, a plastic resinmaterial, PMMA (nd=1.49171, νd=57.4), is used for the first diffractiongrating 3 a. A plastic resin material, PC (nd=1.58306, νd=30.2), is usedfor the second diffraction grating 3 b. An ultraviolet curable resin,HV16 (nd=1.5980, νd=28.0), which is a product of ADEERU Co., is used forthe third diffraction grating 3 c.

[0065] Accordingly, the refractive index n1 of the first diffractiongrating 3 a is 1.50634 at the wavelength of 410 nm, 1.49773 at thewavelength of F-line, and 1.48917 at the wavelength of C-line. Therefractive index n2 of the second diffraction grating 3 b is 1.61362,1.59679 and 1.57750 at these wavelengths, respectively. The refractiveindex n3 of the third diffraction grating 3 c is 1.63482, 1.61319 and1.59183 at these wavelengths, respectively. Therefore, according to theformula (4), there are established the following formulas:

(1.50634−1)d 1+(1.61362−1)d 2+(1.63482−1)d 3=0.41  (6)

(1.49773−1)d 1+(1.59679−1)d 2+(1.61319−1)d 3=0.48607  (7)

(1.48917−1)d 1+(1.57750−1)d 2+(1.59183−1)d 3=0.65627  (8).

[0066] Since there are three variables for these three formulas, thethicknesses of the materials which satisfy all of these formulas can beunivalently obtained. The solution of these formulas gives the values ofgrating thicknesses d1, d2 and d3 as follows: d1=27.50 μm, d2=−36.22 μmand d3=13.73 μm. The grating thickness d2 is in a negative value in thiscase. This means that the purpose of the structural arrangement can beattained by causing the increase and decrease of the grating thicknessd2 to be inverse to those of the other grating thicknesses d1 and d3.The diffraction efficiency η obtained at the wavelength of 410 nm andthe wavelength of F-line and the wavelength of C-line becomes η=1.00,which is a maximum value, because the value inside “( )” of the formula(5) is obtained as “0” from “d0=mλ”.

[0067] The diffraction efficiency for light of other visible wavelengthsis next obtained. Since the grating thickness has already been decided,the diffraction efficiency for each wavelength is computed according tothe formula (5). FIG. 3 shows values of the phase amplitude d(λ)/mλobtained for the respective wavelengths. FIG. 4 shows values of thediffraction efficiency obtained at the design order for the respectivewavelengths. FIG. 5 shows values of the diffraction efficiency obtainedat diffraction orders near the design order (zero and second orders) forthe respective wavelengths.

[0068] As is understandable from FIG. 3, there are three designwavelengths where the phase amplitude becomes “1” within the visiblespectrum. Further, the values of the phase amplitude at wavelengthsother than the design wavelengths do not exceed 5%. This indicates thatthe diffraction efficiency at the design order is excellent and is atleast 99% for the whole region of useful wavelengths. Further, thediffraction efficiency at other diffraction orders near the design order(zero and second orders) is also good as it takes a low value only equalto or less than 0.3%.

[0069] With the materials appositely selected as described above, thediffractive optical element is formed to have a high diffractionefficiency for the whole useful wavelength region.

[0070] The above description shows that a diffractive optical elementwhich is capable of satisfying conditions for attaining the object ofthe invention can be formed by selecting a combination of materials ofthree different kinds. In actually carrying out the invention, however,a search for the combination of materials and the grating thickness ismade in the order of procedures reverse to the description given in theforegoing. For example, a rate of diffraction efficiency as desired isfirst decided. If the desired rate of diffraction efficiency is equal toor above 98%, the diffraction efficiency η can be expressed as follows:

η=sin c ²(d(λ)/mλ−1)≧0.98.

[0071] Then, the diffraction efficiency of at least 98% can be obtainedfor the whole useful wavelength region if “d(λ)/mλ” satisfies thefollowing condition:

0.9217≦d(λ)/mλ≦1.0783  (9).

[0072] The above-stated optical path length difference

d(λ)=(n 1(λ)−1)d 1±(n 2(λ)−1)d 2± . . . ±(nL(λ)−1)dL

[0073] is substituted into the formula (9) to obtain the followingexpression:

0.9217≦{(n 1(λ)−1)d 1±(n 2(λ)−1)d 2± . . .±(nL(λ)−1)dL}/mλ≦1.0783  (10).

[0074] In the last place, a search is made for the refractive index ofmaterials and the grating thickness which satisfy the conditionexpressed by the formula (10) above. Then, the shape of grating and thematerials to be employed are decided according to the result of thesearch. In a case where a rate of diffraction efficiency which is atleast 95%, instead of 98%, is acceptable, the formula (10) becomes asshown below:

0.8755≦{(n 1(λ)−1)d 1±(n 2(λ)−1)d 2± . . .±(nL(λ)−1)dL}/mλ≦1.1245  (11).

[0075] Such a modification increases the kinds of materials which can becombined with each other and thus broadens the range of selection ofsuch materials that are inexpensive and excel in durability.

[0076] In the foregoing, a diffractive optical element having threedesign wavelengths, the three layers of materials and the shape ofgrating have been described. In this case, as apparent from the graph ofthe phase amplitude of FIG. 3, the rate of change in phase amplitude isgreat at shorter wavelengths. Therefore, it is preferable to have atleast two of the three design wavelengths on the shorter wavelength sideof the center wavelength of the useful wavelength region. With thedesign wavelengths arranged in this manner, the value of the phaseamplitude can be lessened over the whole region of useful wavelengthsand the rate of diffraction efficiency can be enhanced.

[0077] The rate of change in phase amplitude can be lessened byarranging a difference in wavelength between the design wavelengths tobe at least 50 nm. By virtue of such an arrangement, even if the phaseamplitude has some error due to a manufacturing error, etc., theeventual change in diffraction efficiency can be lessened.

[0078] The diffraction grating shape has been described by limiting itto a shape obtained within one period of diffraction grating. However,it is known that the diffraction efficiency is basically not affected bythe pitch of diffraction grating. In other words, the arrangement of thefirst embodiment described above is applicable not only to theone-dimensional diffraction grating shown in FIG. 1 but also todiffractive optical elements of any different grating pitch shapes,including a diffractive lens shown in FIG. 6.

[0079] Further, the sectional shapes of grating include a kinoform shapeas shown in FIG. 1 and a stepped shape as shown in FIG. 7. However, theinvention is not limited to these shapes but applies to any other knownshapes.

[0080] However, in the case of the stepped shape shown in FIG. 7, theactual grating thickness dL′ is in the following relation to the gratingthickness dL of the kinoform shape: dL′=dL*(N−1)/N, where N representsthe number of steps of the stepped grating. In a case where thediffractive optical element is in the stepped shape, the actual gratingthickness d′ differs from the grating thickness d used in deciding theoptical path length difference.

[0081] The first embodiment as described above is a diffractive opticalelement having a diffraction grating part arranged on a flat plate.However, the same advantageous effect can be attained by arranging thediffraction grating part on a curved lens.

[0082] In the first embodiment, the first diffraction grating is formedon the base plate. The base plate and the first diffraction grating maybe molded together by molding one and the same material.

[0083] Further, in the first embodiment, the design diffraction order isthe first order. It is, however, not limited to the first order. Withthe design order arranged to be other than the first order, such as thesecond order, the same advantageous effect is attainable by setting acomposite optical path length difference, with respect to at least threewavelengths, in such a way as to have the design wavelengths at thedesired diffraction order.

[0084] Next, a diffractive optical element according to a secondembodiment of the invention is described as follows.

[0085] In the first embodiment, a diffractive optical element havingthree design wavelengths is formed by diffraction gratings in astructure composed of three layers, which are least in number accordingto the invention. For that reason, a grating surface is formed even atthe last end part of the diffraction grating. In the second embodiment,on the other hand, the last end part of its diffraction gratingstructure is arranged to be a flat surface by adding another diffractiongrating 3 d as shown in FIG. 8. In this case, since there is nodiffraction surface at the last end part, the provision of theadditional diffraction grating 3 d obviates the necessity of thearrangement to prevent dust from sticking to a grating groove or to addan anti-reflection coating, so that the second embodiment can be handledmore easily as an element than the first embodiment.

[0086] A diffraction optical element according to a third embodiment ofthe invention is next described.

[0087] In each of the first and second embodiments, the thickness of thethinnest part of each of the second and third diffraction gratings 3 band 3 c is arranged to be “0”. This arrangement has the second and thirddiffraction gratings divided at every grating pitch. In the event ofmanufacture by molding with a mold, such a structural arrangementpresents a problem, because the diffractive optical element cannot bereadily peeled off and transferred from the mold.

[0088] To solve this problem, in the third embodiment, a layer of amaterial which is the same as the material of the second diffractiongrating 3 b is added to the whole area of the diffraction grating part 3with a uniform thickness “doff”, as shown in FIG. 9. By this additionallayer the grating sections of the second diffraction grating 3 b areinterconnected, so that the diffraction grating can be readily peeledoff from a mold in the event of molding by the mold. If the third andfourth diffraction gratings 3 c and 3 d are arranged also in thismanner, all the grating parts can be easily molded.

[0089]FIG. 10 shows as a fourth embodiment of the invention an opticalsystem using a diffractive optical element arranged according to theinvention.

[0090] In FIG. 10, reference numeral 5 denotes a photo-taking lens. Adiaphragm 6 and the diffractive optical element 1 according to theinvention are disposed inside of the photo-taking lens 5. An imageforming plane 7 is a photosensitive surface of a film.

[0091] In this case, the photo-taking lens is set to have apredetermined transmission factor by the sum of the transmission factorof the refractive lens part and the diffraction efficiency (transmissionfactor) of the diffraction grating part which is arranged according tothe invention. In the case of the conventional diffraction grating, thediffraction efficiency (transmission factor) of the diffraction gratingvaries to a considerable degree according to wavelengths as shown inFIG. 13. In order to obtain a spectral characteristic required for aphoto-taking lens, therefore, it has been necessary to use a filter suchas a dichroic coating for correcting the transmission characteristic ofthe diffractive optical element. Further, in order to make the spectralcharacteristic into the desired characteristic, it is necessary tocorrect only the color of the spectral characteristic of a compositetransmission by dropping the quantity of diffraction light ofwavelengths near the design wavelength. As a result, it has beeninevitable to have a relatively large amount of loss in the quantity oflight.

[0092] According to the invention, on the other hand, the diffractiveoptical element is arranged to retain its diffraction efficiency at ahigh rate for the useful wavelength region. Therefore, the diffractiveoptical element can be handled in the same manner as an ordinaryrefractive lens without necessitating use of any special coating.Further, since the diffraction efficiency at orders near the designorder of diffraction is adequately suppressed, the generation of flarelight under the unusual photo-taking condition mentioned in theforegoing can be greatly reduced.

[0093] In the case of FIG. 10, the diffractive optical element isdisposed on a plate glass surface in the neighborhood of the diaphragm.However, the position of the diffractive optical element is not limitedto this position. The diffractive optical element may be arranged on acurved lens surface, such as a convex or concave surface. It is alsopossible to use a plurality of diffractive optical elements within thephoto-taking lens.

[0094] In the case of the fourth embodiment, the invention is applied tothe photo-taking lens of a camera. However, the invention is not limitedto this. The same advantageous effect can be attained by applying theinvention to a photo-taking lens of a video camera, an image scanner ofa business machine, a reader lens of a digital copying machine, etc.

[0095]FIG. 11 is a sectional view showing as a fifth embodiment of theinvention an optical system using a diffractive optical element arrangedaccording to the invention.

[0096] The optical system shown in FIG. 11 is an observation opticalsystem of a binocular or the like. The observation optical systemincludes an objective lens 8, an image inverting prism 9 for erecting animage, an eyepiece lens 10, and an evaluation plane (pupil surface) 11.In FIG. 11, reference numeral 1 denotes a diffractive optical elementarranged according to the invention. The diffractive optical element 1is provided for the purpose of correcting a chromatic aberration, etc.,of the objective lens 8 on the image forming plane 7.

[0097] In the case of the fifth embodiment, the diffractive opticalelement 1 is disposed on the side of the objective lens 8. However, theposition of the diffractive optical element 1 is not limited to thisposition. The same effect can be attained by setting the diffractiveoptical element 1 on the surface of the prism 9 or inside of theeyepiece lens 10. However, with the diffractive optical element 1 set onthe object side of the image forming plane 11, it serves to abate achromatic aberration caused solely by the objective lens 8. Therefore,in the case of an observation system for observation with the eye, it ispreferable to have the diffractive optical element 1 set at least on theside of the objective lens.

[0098] Further, in the case of the fifth embodiment, the invention isapplied to a binocular. However, the same effect is attainable byapplying the invention to a terrestrial or astronomical telescope or toan optical viewfinder of a lens-shutter camera, a video camera, or thelike.

[0099] According to the arrangement of each embodiment disclosed, aplurality of diffraction gratings are appositely laminated on a baseplate. By this arrangement, a diffractive optical element and an opticalsystem having the diffractive optical element can be arranged to have ahigh rate of diffraction efficiency to lessen unevenness of color overthe whole useful wavelength region.

1. A diffractive optical element formed by laminating at least three layers of diffraction gratings made of at least three kinds of materials which differ in dispersion, wherein at least three design wavelengths are set.
 2. A diffractive optical element according to claim 1, wherein said at least three layers of diffraction gratings are laminated on a base plate, and, letting said diffraction gratings be assumed to be a first diffraction grating, a second diffraction grating and an L-th diffraction grating, as counted from the base plate, a grating thickness of the first diffraction grating be denoted by d1, a grating thickness of the second diffraction grating be denoted by d2, a grating thickness of the L-th diffraction grating be denoted by dL, a refractive index of the first diffraction grating at a wavelength λ be denoted by n1(λ), a refractive index of the second diffraction grating at the wavelength λ be denoted by n2(λ), a refractive index of the L-th diffraction grating at the wavelength λ be denoted by nL(λ), an arbitrary wavelength within a useful wavelength region be denoted by λ0, and a design order of diffraction be denoted by m, the following condition is satisfied: 0.9217≦{(n 1(λ0)−1)d 1±(n 2(λ0)−1)d 2± . . . ±(nL(λ0)−1)dL}/mλ0 ≦1.0783.
 3. A diffractive optical element according to claim 1, wherein said at least three layers of diffraction gratings are laminated on a base plate, and, letting said diffraction gratings be assumed to be a first diffraction grating, a second diffraction grating and an L-th diffraction grating, as counted from the base plate, a grating thickness of the first diffraction grating be denoted by d1, a grating thickness of the second diffraction grating be denoted by d2, a grating thickness of the L-th diffraction grating be denoted by dL, a refractive index of the first diffraction grating at a wavelength λ be denoted by n1(λ), a refractive index of the second diffraction grating at the wavelength λ be denoted by n2(λ), a refractive index of the L-th diffraction grating at the wavelength λ be denoted by nL(λ), an arbitrary wavelength within a useful wavelength region be denoted by λ0, and a design order of diffraction be denoted by m, the following condition is satisfied: 0.8755≦{(n 1(λ0)−1)d 1±(n 2(λ0)−1)d 2± . . . ±(nL(λ0)−1)dL}/mλ0≦1.1245.
 4. A diffractive optical element according to claim 1, wherein the design wavelengths include at least two design wavelengths which are shorter than a center wavelength of a useful wavelength region.
 5. A diffractive optical element according to claim 4, wherein the useful wavelength region is a visible spectrum.
 6. A diffractive optical element according to claim 1, wherein said diffraction gratings made of at least three kinds of materials which differ in dispersion include at least one kind of grating structure whose grating thickness within one period monotonously increases between materials which differ in dispersion and at least one kind of grating structure whose grating thickness within one period monotonously decreases between materials which differ in dispersion.
 7. A diffractive optical element according to claim 2, wherein said first diffraction grating and said base plate are made of the same material.
 8. A diffractive optical element according to claim 3, wherein said first diffraction grating and said base plate are made of the same material.
 9. A diffractive optical element formed by laminating a first diffraction grating, a second diffraction grating and an L-th diffraction grating, wherein, letting a grating thickness of the first diffraction grating be denoted by d1, a grating thickness of the second diffraction grating be denoted by d2, a grating thickness of the L-th diffraction grating be denoted by dL, a refractive index of the first diffraction grating at a wavelength λ be denoted by n1(λ), a refractive index of the second diffraction grating at the wavelength be denoted by n2(λ), a refractive index of the L-th diffraction grating at the wavelength λ be denoted by nL(λ), an arbitrary wavelength within a useful wavelength region be denoted by λ0, and a design order of diffraction be denoted by m, the following condition is satisfied: 0.9217≦{(n 1(λ0)−1)d 1±(n 2(λ0)−1)d 2± . . . ±(nL(λ0)−1)dL}/mλ0≦1.0783.
 10. A diffractive optical element according to claim 9, wherein the useful wavelength region is a visible spectrum.
 11. A diffractive optical element formed by laminating a first diffraction grating, a second diffraction grating and an L-th diffraction grating, wherein, letting a grating thickness of the first diffraction grating be denoted by d1, a grating thickness of the second diffraction grating be denoted by d2, a grating thickness of the L-th diffraction grating be denoted by dL, a refractive index of the first diffraction grating at a wavelength λ be denoted by n1(λ), a refractive index of the second diffraction grating at the wavelength λ be denoted by n2(λ), a refractive index of the L-th diffraction grating at the wavelength λ be denoted by nL(λ), an arbitrary wavelength within a useful wavelength region be denoted by λ0, and a design order of diffraction be denoted by m, the following condition is satisfied: 0.8755≦{(n 1(λ0)−1)d 1±(n 2(λ0)−1)d 2± . . . ±(nL(λ0)−1)dL}/mλ0≦1.1245.
 12. A diffractive optical element according to claim 11, wherein the useful wavelength region is a visible spectrum.
 13. An optical system comprising a diffractive optical element according to one of claims 1 to
 12. 14. An optical system according to claim 13, wherein said optical system is an image forming optical system.
 15. An optical system according to claim 13, wherein said optical system is an observation optical system.
 16. A camera comprising an optical system according to claim
 13. 17. An optical apparatus comprising an optical system according to claim
 13. 